The Kahler package is a collection of three properties - Poincare duality, Hard Lefschetz, and the Hodge-Riemann relations - of graded artinian R-algebras equipped with an open convex cone in the degree one part. Certain rings, which are related to matroids and look like the cohomology rings of projective bundles, are expected to have the Kahler package. I will explain how to show that there is some cone for which they have the Kahler package, and how to get control over this cone in certain cases. Joint with Christopher Eur and June Huh.